Searching a table both horizontally and vertically and printing the values - excel

Question

sorry for the ambiguous title. I'm not quite sure how to name what I'm trying to do.
I have data in a worksheet that looks like this:
I would like to search for the smallest number in the range and write out the name on the y axis and the number. It then ignores this number and searches for the smallest number on the x axis as well. In that same row, it searches for the smallest value horizontally, excludes the number and then looks vertically as well. It continues this way until all possibilities are exhausted. Is this possible with Excel?
A sample output will be:
y5 : 40
x3: 60
y3: 90
x4: 80
y2 : 85
x3: 75
y1 : 70
and so on.

Answer 1

Interesting problem. You should be able to modify the following. To run it you need to include a reference to Microsoft Scripting Runtime (Under Tools/References in the VBA editor) since it uses a dictionary data structure -- the natural choice to keep track of already picked numbers:
'The following code assumes than Nums is a 1-based 2-dimensional array
Function MinPath(Nums As Variant) As Variant
Dim counter As Long
Dim mins As Variant
Dim PickedNums As New Dictionary
Dim i As Long, j As Long, m As Long, n As Long
Dim report As String
Dim direction As String
Dim num As Variant
Dim min As Variant, min_i As Long, min_j As Long
m = UBound(Nums, 1)
n = UBound(Nums, 2)
ReDim mins(1 To m * n)
min = Nums(1, 1)
min_i = 1
min_j = 1
For i = 1 To m
For j = 1 To n
If Nums(i, j) < min Then
min = Nums(i, j)
min_i = i
min_j = j
End If
Next j
Next i
PickedNums.Add min, 0
counter = 1
mins(counter) = Array(min_i, min_j, min)
direction = "vertical"
min = Empty
Do While True
If direction = "vertical" Then
For i = 1 To m
num = Nums(i, min_j)
If Not PickedNums.Exists(num) Then
If IsEmpty(min) Then
min = num
min_i = i
ElseIf num < min Then
min = num
min_i = i
End If
End If
Next i
If IsEmpty(min) Then
ReDim Preserve mins(1 To counter)
MinPath = mins
Exit Function
Else
PickedNums.Add min, 0
counter = counter + 1
mins(counter) = Array(min_i, min_j, min)
direction = "horizontal"
End If
Else
'direction = horizontal case
For j = 1 To n
num = Nums(min_i, j)
If Not PickedNums.Exists(num) Then
If IsEmpty(min) Then
min = num
min_j = j
ElseIf num < min Then
min = num
min_j = j
End If
End If
Next j
If IsEmpty(min) Then
ReDim Preserve mins(1 To counter)
MinPath = mins
Exit Function
Else
PickedNums.Add min, 0
counter = counter + 1
mins(counter) = Array(min_i, min_j, min)
direction = "vertical"
End If
End If
min = Empty
Loop
End Function
The function repeatedly searches a either a row or a column (depending on the search direction) to find the smallest non-picked number. At the beginning of each pass the variable min is set to Empty until a non-picked number is encountered. If after a pass min is still Empty the function returns. This function returns an array of arrays where each array is of the form Array(i,j,min) (e.g. the values (5,3,40) in the first step). VBA's Array function returns a 0-based array so the i (row) coordinate is at index 0 and the j coordinate is at index 1. What you do with this data is up to you. For example:
Sub test()
Dim i As Long, n As Long
Dim mins As Variant
mins = MinPath(Range("B2:F6").Value)
n = UBound(mins)
For i = 1 To n
If i Mod 2 = 1 Then 'odd step
Range("A7").Offset(i).Value = "y" & mins(i)(0) & ":"
Else 'even step
Range("A7").Offset(i).Value = "x" & mins(i)(1) & ":"
End If
Range("B7").Offset(i).Value = mins(i)(2)
Next i
End Sub
Which results in: